The Ericksen-Leslie theory describes the dynamic flow of liquid crystals. In this talk, we will discuss global existence of solutions of the Ericksen-Leslie system for a general Oseen-Frank model in 2D. We also discuss some new results on the local existence, uniqueness and the blow up criterions of strong solutions to the Ericksen-Leslie system in 3D for the general Oseen-Frank model in 3D.

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